IMO 1976 LL USA36

Three concentric circles with common center O are cut by a

IMO 1976 LL USA36

Origin: USA

Problem

Three concentric circles with common center O are cut by a common chord in successive points A, B, C. Tangents drawn to the circles at the points A, B, C enclose a triangular region. If the distance from point O to the common chord is equal to p, prove that the area of the region enclosed by the tangents is equal to AB \cdot BC \cdot CA 2p .